The Texans learned their lesson last Monday night: The New England Patriots do not lose at home in December.

The Texans discovered to their astonishment Sunday night that the Patriots do lose at home in December.

The Patriots came back from a 31-3 deficit against the visiting San Francisco 49ers to tie, only to fall, 41-34, at Gillette Stadium, reestablishing the Texans as a strong favorite to earn home-field advantage throughout the AFC playoffs. The Texans were blown out there, 42-14, six days before, giving the Patriots their 20th consecutive victory at home in December.

Now the Texans have some breathing room after the 49ers’ breathtaking victory.

“You don’t want to ever have to watch the scoreboard,” Texans center Chris Myers said. “That’s how it was around here the previous couple years, watching the scoreboard and hoping other teams would lose to get you into the playoffs. As long as you take care of it yourself, it’s one of the most gratifying things.”

The Texans took care of all they could Sunday, winning 29-17 over Indianapolis at Reliant Stadium for a 12-2 record.

The Denver Broncos are at this point second seeded in the AFC at 11-3.

The Patriots fell to 10-4.

All the Texans need to do to secure home-field advantage is to win one more regular season game, either at home next Sunday or on Jan. 30 at Indianapolis.

That would eliminate Denver because the Texans hold the tiebreaking advantage over the Bronocs, having beaten them head-to-head early in the season.

That would eliminate New England because the Texans would finish the season with a better record.

The Texans also would secure home-field advantage if either Denver or New England lose one of their final two games.

The Texans could fail to earn a first-round bye only by losing both remaining games while Denver and New England win theirs.

Home-field advantage doesn’t guarantee a Super Bowl berth, but it’s a lot easier than having to play in either Denver or New England in January to get to the Super Bowl in New Orleans.